The present invention relates to discrete cosine transforms, and more particularly, to an engine for performing discrete cosine transforms.
It is desirable to compress image signals which are used with computer systems as an image signal for a single uncompressed high resolution digitized color image can easily fill several megabytes of storage. Because images generally have low information content, very good compression rates are possible. This is especially true if, as is often the case with image signals which are used with computer systems, perfect reproduction is not required. When perfect reproduction is not required, the low frequency components of a frequency domain image signal are perceptually more important in reproducing the image than the high frequency components of the frequency domain image signal. Thus, compression schemes that are applied to the frequency domain version of an image signal do not waste unnecessary bits in accurately representing the high frequency portions of the image signal.
Accordingly, it is desirable to transform an image signal from the spacial domain to the frequency domain prior to compressing the image signal. One type of transform that is desirable when transforming image signals is the discrete cosine transform (DCT). Examples of compression schemes which use a DCT include a Joint Photographics Experts Group standard (JPEG), a Moving Pictures Expert Group standard (MPEG), and a Consulting Committee for International Telegraphy and Telephony standard (CCITTH.261). A DCT is similar to a Fourier transform; an 8.times.8 DCT can be computed as a 16.times.16 Fourier transform. A DCT includes a pair of transforms, a forward DCT (FDCT), which maps a digitized signal to a frequency domain signal, and an inverse DCT (IDCT), which maps a frequency domain signal to a digitized signal.
It is known to perform DCT's in software on a personal computer to compress and decompress an image signal. When transforming a color image signal compared to a monochrome image signal, the amount of computation required increases by a factor of three. Additionally, the amount of computation required to transform an image increases as the square of the size of the screen of the computer.
When compressing an image signal, it is desirable to perform the DCTs quickly as compressing an image signal requires many DCTs to be performed. For example, to perform a JPEG compression of a 1024 by 1024 pixel color image requires 49,152 8.times.8 DCT's. If 30 images are compressed or decompressed every second, as is suggested to provide full motion video, then a DCT must be performed every 678 nsec. The calculation of a single 8.times.8 DCT (using the standard definition of a DCT transform) requires more that 9200 multiplications and more than 4000 additions.
It is known to perform DCTs on a matrix of data by first transforming the rows of data and then convolving the transformed rows to provide a transformed matrix of data. Such a system is relatively slow as the system includes the extra step of convolving the transformed rows of data.